# New Tools and Connections for Exponential-Time Approximation

@article{Bansal2018NewTA,
title={New Tools and Connections for Exponential-Time Approximation},
author={N. Bansal and Parinya Chalermsook and B. Laekhanukit and Danupon Nanongkai and Jesper Nederlof},
journal={Algorithmica},
year={2018},
volume={81},
pages={3993 - 4009}
}
AbstractIn this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and an integer $$r>1$$r>1, and the goal is to design an approximation algorithm with the fastest possible running time. We give randomized algorithms that establish an approximation ratio of1.r for maximum independent set in $$O^*(\exp ({\tilde{O}}(n/r \log ^2 r+r\log ^2r)))$$O∗(exp(O~(n/rlog2r+rlog2r))) time,2.r for chromatic number in O^*(\exp… Expand

#### References

SHOWING 1-10 OF 45 REFERENCES
• Mathematics, Computer Science
• J. Comput. Syst. Sci.
• 2018
• Mathematics, Computer Science
• STACS
• 2016
Exact and approximate bandwidth
• Computer Science, Mathematics
• Theor. Comput. Sci.
• 2010
Exponential-time approximation of weighted set cover
• Mathematics, Computer Science
• Inf. Process. Lett.
• 2009
Exponential-Time Approximation of Hard Problems
• Computer Science, Mathematics
• ArXiv
• 2008
Free Bits, PCPs, and Nonapproximability-Towards Tight Results
• Mathematics, Computer Science
• SIAM J. Comput.
• 1998
Mildly exponential reduction from gap 3SAT to polynomial-gap label-cover
• Irit Dinur
• Computer Science, Mathematics
• Electron. Colloquium Comput. Complex.
• 2016